scholarly journals Tauberian theorems in the case of absolute summability in degree $p$ of double series

2021 ◽  
pp. 90
Author(s):  
T.N. Yarkovaia
Keyword(s):  
Tauberian Theorem ◽  
Double Series ◽  
Absolute Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

We establish a Tauberian theorem in the case of absolute summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

scholarly journals Tauberian theorems in the case of strong summability in degree $p$ of double series

2021 ◽  
pp. 84
Author(s):  
T.N. Yarkovaia
Keyword(s):  
Tauberian Theorem ◽  
Double Series ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

We establish a Tauberian theorem in the case of strong summability in degree $p$ of double series by matrix methods, give its application to Abel methods.

Absolute Summability Factors and Absolute Tauberian Theorems for Double Series and Sequences

1999 ◽  
Vol 6 (6) ◽  
pp. 591-600
Author(s):  
Sh. Yanetz (Chachanashvili)
Keyword(s):  
Double Series ◽  
Absolute Summability ◽  
Tauberian Theorems ◽  
Summability Factors ◽  
Tauberian Conditions ◽  
Absolute Summability Factors

Abstract Let 𝐴 and 𝐵 be the linear methods of the summability of double series with fields of bounded summability and , respectively. Let 𝑇 be certain set of double series. The condition 𝑥 ∈ 𝑇 is called 𝐵𝑏-Tauberian for 𝐴 if . Some theorems about summability factors enable one to find new 𝐵𝑏-Tauberian conditions for 𝐴 from the already known 𝐵𝑏-Tauberian conditions for 𝐴.

Strong summability of double series by matrix methods and Tauberian theorems for these methods

1975 ◽  
Vol 17 (3) ◽  
pp. 227-232
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Double Series ◽  
Strong Summability ◽  
Tauberian Theorems ◽  
Matrix Methods

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

Tauberian theorems for absolute summability

1997 ◽  
pp. 195-201
Author(s):  
G. G. Lorentz
Keyword(s):  
Absolute Summability ◽  
Tauberian Theorems

scholarly journals Absolute summability of power $p$ of series, associated with conjugate Fourier series, by triangular matrix methods

2021 ◽  
pp. 54
Author(s):  
N.I. Volkova ◽  
N.S. Novikova
Keyword(s):  
Fourier Series ◽  
Triangular Matrix ◽  
Absolute Summability ◽  
Matrix Methods ◽  
Conjugate Fourier Series

We establish conditions of absolute summability of powers of series that are associated with conjugate Fourier series, by triangular matrix methods, and provide the application of the theorems proved to Voronoi-Nerlund method.

New Tauberian Theorems from Old

1994 ◽  
Vol 46 (2) ◽  
pp. 380-394
Author(s):  
Mangalam R. Parameswaran
Keyword(s):  
Absolute Summability ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Tauberian Conditions ◽  
Powerful Approach ◽  
Abstract Spaces

AbstractA new and very general and simple, yet powerful approach is introduced for obtaining new Tauberian theorems for a summability method V from known Tauberian conditions for V, where V is merely assumed to be linear and conservative. The technique yields the known theorems on the weakening of Tauberian conditions due to Meyer-König and Tietz and others and also improves many of them. Several new results are also obtained, even for classical methods of summability, including analogues of Tauber's second theorem for the Borel and logarithmic methods. The approach yields also new Tauberian conditions for the passage from summability by a method V to summability by a method V', as well as to more general methods of summability like absolute summability or summability in abstract spaces; the present paper however confines itself to ordinary summability.

A Tauberian theorem for the summation of double series by Borel's method

1988 ◽  
Vol 39 (6) ◽  
pp. 653-655
Author(s):  
K. M. Slepenchuk
Keyword(s):  
Tauberian Theorem ◽  
Double Series

A Tauberian Theorem for the General Euler-Borel Summability Method

1992 ◽  
Vol 44 (5) ◽  
pp. 1100-1120 ◽  
Author(s):  
Laying Tam
Keyword(s):  
Positive Integer ◽  
Unit Disk ◽  
Tauberian Theorem ◽  
Summability Method ◽  
Tauberian Theorems ◽  
Borel Summability ◽  
Closed Unit Disk ◽  
Tauberian Condition ◽  
Image Position ◽  
General Conditions

AbstractOur main result is a Tauberian theorem for the general Euler-Borel summability method. Examples of the method include the discrete Borel, Euler, Meyer- Kônig, Taylor and Karamata methods. Every function/ analytic on the closed unit disk and satisfying some general conditions generates such a method, denoted by (£,ƒ). For instance the function ƒ(z) = exp(z — 1) generates the discrete Borel method. To each such function ƒ corresponds an even positive integer p = p(f).We show that if a sequence (sn)is summable (E,f)and as n→ ∞ m > n, (m— n)n-p(f)→0, then (sn)is convergent. If the Maclaurin coefficients of/ are nonnegative, then p(f) =2. In this case we may replace the condition . This generalizes the Tauberian theorems for Borel summability due to Hardy and Littlewood, and R. Schmidt. We have also found new examples of the method and proved that the exponent —p(f)in the Tauberian condition (*) is the best possible.

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